The angular speed of the Earth decreases with time. This pace is indicated by the observations of the occurrences of solar eclipse during this period. Let us assume that the length of the day uniformly increases by 0.001 s per century. Calculate the cumulative effect on the measure of time for a period of 10 centuries. (Express it in seconds).

Assuming the length of the day uniformly increases by 0.001 second per century. Calculate the net effect on the measure of time over 20 centuries.

A large number of pendulums with identical bobs (mass m) but varying lengths are suspended from a thick thread. Another pendulum of a heavier bob (mass M) is also suspended from the same thred as shown. This pendulum with the heavier bob is used as a 'driver' to drive the other pendulums called as 'driven' pendulums. Assume that the amplitude of the driver is maintained constant (by some suitable mechanism). Let the frequency of the driver be f_(0) The time periods - hence the frequencies (f) and the amplitudes (A) of the driven pendulums in steady state are measured. The variation of A wil f is correctly shown by the graph.

If the length of a seconds pendulum is first decreased by 10 cm and its time period is determined and then increased by 20 cm and the time period is once again determined, find the ratio of the time periods in two cases. (Take g = 9.8 m s^(-2) )

When the sun appears to be just on horizon, it is in fact below the horizon. This is because the light from the sun bends when it enters the earth’s atmosphere. Let us assume that atmosphere is uniform and has index of refraction equal to mu . It extends upto a height h (lt lt R = radius of earth) above the earth’s surface. In absence of atmosphere how late would we see the sunrise compared to what we see now? Take time period of rotation of earth to be T. Calculate this time for following data R = 6400km, mu = 1.0003, h = 20 km, T = 24hr .

Two boys are holding a wire, standing 4 m apart. The wire sags in the shape of a circular arc with a sag of 1.0 m. The students rotate the wire about the horizontal line connecting their hands, as if they were playing jump rope. The boys rotate the wire at a speed of 4 revolutions per second. The earth’s magnetic field at the location is 4 xx 10^(– 5) T. Calculate the rms value of emf developed between the ends of the wire. Assume that the shape of the wire is maintained as it is rotated.

A block is kept in a room which is at 20^(@)C . To raise the temperature of the block, heat is given to it at a constant rate of 600 watt (using an electric heater). The temperature of the block rises with time as shown in the graph. The slope of the graph at time t = 0 is 3^(@)C s^(-1) . Once the temperature rises to 60^(@)C , the heater is switched off and another heater is switched on to maintain the temperature of the block at 60^(@)C . This new heater supplies heat at a constant rate of 100 watt. Assume that heat capacity of the block remains constant for the range of temperature involved. (a) Explain why the slope of the given graph is decreasing with time. (b) Calculate the heat capacity of the block. (c) If the 100 W heater is also switched off, what will be initial rate of cooling of the block? (d) Assuming that rate of heat loss by the block to the surrounding is proportional to difference in its temperature with surrounding, calculate the heat radiated per second by the block when it was at 30^(@)C .